IJPAM: Volume 115, No. 1 (2017)

Title

A NOTE ON UNSTEADY HYDROMAGNETIC FLOW DUE
TO TANGENTIAL STRESS AT THE HORIZONTAL
FREE SURFACE

Authors

K. Jagadeshkumar$^1$, Vempaty Somaraju$^2$, S. Srinivas$^1$
$^1$Department of Mathematics
School of Advanced Sciences
VIT University, Vellore, Tamil Nadu, INDIA
$^2$Department of Mathematics,LIAS
GVP College of Engineering (Autonomous)
Vishakhapatnam, Andhra Pradesh, INDIA

Abstract

The problem of unsteady unidirectional hydromagnetic flow due to stress applied at the free surface is studied here. The applied magnetic field is normal to the horizontal boundary. The dynamics of fluid and electric currents are investigated as functions of magnetic Prandtl number $P_{m} \,(=\sigma \mu_{0} \nu )$, which measures the ratio of viscous diffusion to magnetic diffusion. In contrast to hydrodynamic Rayleigh problem, the transient dynamics consists of two diffusively growing layers as in the conventional MHD Rayleigh problem (see Dix [5]). The viscous Hartmann layer becomes steady soon, while the magnetic diffusion layer diffuses to infinity with Alfven speed. The electric currents generated in the Hartmann layer find a return path in the magnetic diffusion layer. It may also be seen that the free surface Hartmann layer is weak compared to rigid surface Hartmann layer.

History

Received: December 15, 2016
Revised: May 30, 2017
Published: June 29, 2017

AMS Classification, Key Words

AMS Subject Classification: 76W
Key Words and Phrases: magnetohydrodynamics, Hartmann layer, magnetic Prandtl number

Download Section

Download paper from here.
You will need Adobe Acrobat reader. For more information and free download of the reader, see the Adobe Acrobat website.

Bibliography

1
G.K. Batchelor, An Introduction to Fluid Dynamics, Cambridge University Press, Cambridge, 1993.

2
E.R. Benton, D.E. Loper, On the spin-up of an electrically conducting fluid Part 1. The unsteady hydromagnetic Ekman-Hartmann boundary layer problem, J. Fluid Mech., 39 (1969), 561-586.

3
G.A. Campbell, R.M. Foster, Fourier Integrals for Practical Applications, D. Van Nostrand Company, Inc, New York (1948).

4
C.C. Chang, J.T. Yen, Rayleigh's problem in magnetohydrodynamics, Phys. Fluids, 2 (1959), 393-403.

5
D.M. Dix, The magnetohydrodynamic flow past a non-conducting flat plate in the presence of a transverse magnetic field, J. Fluid Mech., 15 (1963), 449-476.

6
W.F. Hughes, F.J. Young, The Electromagnetodynamics of Fluids, John Wiley & Sons, New York, 1966.

7
J. Pedlosky, Geophysical Fluid Dynamics, Springer-Verlag, 1972.

8
V.J. Rossow, On Rayleigh's problem in magnetohydrodynamics, Phys. Fluids , 3 (1960), 395.

9
S. Vempaty, R. Balasubramanian, Ekman-Hartmann layer on a free surface, Indian J. Pure appl. Math., 18, No. 5 (1987), 442-450.

How to Cite?

DOI: 10.12732/ijpam.v115i1.2 How to cite this paper?

Source:
International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2017
Volume: 115
Issue: 1
Pages: 13 - 25


Google Scholar; DOI (International DOI Foundation); WorldCAT.

CC BY This work is licensed under the Creative Commons Attribution International License (CC BY).